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Articles 1981 - 2010 of 2456

Full-Text Articles in Physical Sciences and Mathematics

Lake Whatcom Monitoring Project 2005/2006 Report, Robin A. Matthews, Michael Hilles, Joan Vandersypen, Robert J. Mitchell, Geoffrey B. Matthews Apr 2007

Lake Whatcom Monitoring Project 2005/2006 Report, Robin A. Matthews, Michael Hilles, Joan Vandersypen, Robert J. Mitchell, Geoffrey B. Matthews

Lake Whatcom Annual Reports

This report is part of an on-going series of annual reports and special project reports that document the Lake Whatcom monitoring program. This work is conducted by the Institute for Watershed Studies and other departments at Western Washington University.

The major objective of this program is to provide long-term baseline water quality monitoring in Lake Whatcom and selected tributaries. Each section contains brief explanations about the water quality data, along with discussions of patterns observed in Lake Whatcom.


Restoration Of Rivers Used For Timber Floating: Effects On Riparian Plant Diversity, James M. Helfield, Samantha Capon, Christer Nilsson, Roland Jansson, Daniel Palm Apr 2007

Restoration Of Rivers Used For Timber Floating: Effects On Riparian Plant Diversity, James M. Helfield, Samantha Capon, Christer Nilsson, Roland Jansson, Daniel Palm

Environmental Sciences Faculty and Staff Publications

Fluvial processes such as flooding and sediment deposition play a crucial role in structuring riparian plant communities. In rivers throughout the world, these processes have been altered by channelization and other anthropogenic stresses. Yet despite increasing awareness of the need to restore natural flow regimes for the preservation of riparian biodiversity, few studies have examined the effects of river restoration on riparian ecosystems. In this study, we examined the effects of restoration in the Ume River system, northern Sweden, where tributaries were channelized to facilitate timber floating in the 19th and early 20th centuries. Restoration at these sites involved the …


Perturbations Of Roots Under Linear Transformations Of Polynomials, Branko Ćurgus, Vania Mascioni Apr 2007

Perturbations Of Roots Under Linear Transformations Of Polynomials, Branko Ćurgus, Vania Mascioni

Mathematics Faculty Publications

Let Pn be the complex vector space of all polynomials of degree at most n. We give several characterizations of the linear operators T:Pn→Pn for which there exists a constant C > 0 such that for all nonconstant f∈Pn there exist a root u of f and a root v of Tf with |u−v|≤C. We prove that such perturbations leave the degree unchanged and, for a suitable pairing of the roots of f and Tf, the roots are never displaced by more than a uniform constant independent on f. We show that such "good" operators T …


The Planet, 2007, Spring, Shawn C. Query, Huxley College Of The Environment, Western Washington University Apr 2007

The Planet, 2007, Spring, Shawn C. Query, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.


The Effect Of Sculpin Presence On Benthic Macroinvertebrate Abundances In Chuckanut Creek, Washington, Sam Stoner Apr 2007

The Effect Of Sculpin Presence On Benthic Macroinvertebrate Abundances In Chuckanut Creek, Washington, Sam Stoner

WWU Honors College Senior Projects

Sculpins are one of the most abundant fishes in Pacific coastal streams and lakes, but they remain understudied despite potentially significant impacts to stream ecology. The poor swimming ability of sculpins limits their range by inhibiting passage of barriers passable to other fishes. Sculpins are voracious eaters and feed primarily on stream invertebrates. By sampling invertebrates in reaches of stream above and below a sculpin barrier, this study examined the impact sculpin presence had on the stream invertebrate community. Invertebrates were sampled in riffles using a Serber sampler (n = 4). The results showed that the presences of sculpins had …


Zwitterionic Self-Assembly Of L-Methionine Nanogratings On The Ag(111) Surface, Andreas Riemann, Agustin Schiffrin, Willi Auwarter, Yan Pennec, Alex Weber-Bargioni, Albano Cossaro, Alberto Morgante, Johannes V. Barth Mar 2007

Zwitterionic Self-Assembly Of L-Methionine Nanogratings On The Ag(111) Surface, Andreas Riemann, Agustin Schiffrin, Willi Auwarter, Yan Pennec, Alex Weber-Bargioni, Albano Cossaro, Alberto Morgante, Johannes V. Barth

Physics & Astronomy

The engineering of complex architectures from functional molecules on surfaces provides new pathways to control matter at the nanoscale. In this article, we present a combined study addressing the self-assembly of the amino acid L-methionine on Ag(111). Scanning tunneling microscopy data reveal spontaneous ordering in extended molecular chains oriented along high-symmetry substrate directions. At intermediate coverages, regular biomolecular gratings evolve whose periodicity can be tuned at the nanometer scale by varying the methionine surface concentration. Their characteristics and stability were confirmed by helium atomic scattering. X-ray photoemission spectroscopy and high-resolution scanning tunneling microscopy data reveal that the L-methionine chaining is …


Volcanic Eruptions At East Pacific Rise Near 9°50'N, James P. Cowen, Brooke Love, Brian Glazier, Daniel J. Fornari, Timothy M. (Timothy Mitchell) Shank, S. Adam Soule, Alexander Treusch, Kyle R. Pomranig, R. Chadwick Holmes, Maya Tolstoy, Edward T. Baker Feb 2007

Volcanic Eruptions At East Pacific Rise Near 9°50'N, James P. Cowen, Brooke Love, Brian Glazier, Daniel J. Fornari, Timothy M. (Timothy Mitchell) Shank, S. Adam Soule, Alexander Treusch, Kyle R. Pomranig, R. Chadwick Holmes, Maya Tolstoy, Edward T. Baker

Environmental Sciences Faculty and Staff Publications

Evidence for recent volcanic eruptions along the fast spreading East Pacific Rise (EPR) crest near 9°50'N spanning about 4 to 5 months of activity was discovered in April and May 2006 as a result of studies related to the U.S. National Science Foundation's (NSF) Ridge2000 (R2K) program. In April, during routine recovery and redeployment of ocean-bottom seismometers (OBS) at the EPR R2K Integrated Study Site (ISS) near 9°50'N, eight of 12 OBS could not be recovered [Tolstoy et al, 2006]. Anomalous turbidity and temperature structure in the water column along the ridge axis confirmed scientists' suspicions that the OBS were …


Geomorphic Constraints On Listric Thrust Faulting: Implications For Active Deformation In The Mackenzie Basin, South Island, New Zealand, Colin Amos, Douglas W. Burbank, David C. Nobes, Stuart A. L. Read Feb 2007

Geomorphic Constraints On Listric Thrust Faulting: Implications For Active Deformation In The Mackenzie Basin, South Island, New Zealand, Colin Amos, Douglas W. Burbank, David C. Nobes, Stuart A. L. Read

Geology Faculty Publications

Deformed fluvial terraces preserved over active thrust-related folds record the kinematics of folding as fault slip accumulates on the underlying thrust. In the Mackenzie Basin of southern New Zealand, the kinematics revealed by folded fluvial terraces along the active Ostler and Irishman Creek fault zones are inconsistent with traditional models for thrust-related folding in which spatially uniform rock uplift typically occurs over planar fault ramps. Instead, warped and tilted terraces in the Mackenzie are characterized by broad, continuous backlimbs and abrupt forelimbs and suggest folding through progressive limb rotation. By relating this pattern of surface deformation to the underlying thrust …


An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett Feb 2007

An Unexpected Limit Of Expected Values, Branko Ćurgus, Robert I. Jewett

Mathematics Faculty Publications

Let t⩾0. Select numbers randomly from the interval [0,1] until the sum is greater than t . Let α(t) be the expected number of selections. We prove that α(t)=et for 0⩽t⩽1. Moreover, . This limit is a special case of our asymptotic results for solutions of the delay differential equation f(t)=f(t)-f(t-1) for t>1. We also consider four other solutions of this equation that are related to the above selection process.


On A Convex Operator For Finite Sets, Branko Ćurgus, Krzysztof Kołodziejczyk Jan 2007

On A Convex Operator For Finite Sets, Branko Ćurgus, Krzysztof Kołodziejczyk

Mathematics Faculty Publications

Let S be a finite set with m elements in a real linear space and let be a set of m intervals in . We introduce a convex operator which generalizes the familiar concepts of the convex hull, , and the affine hull, , of S . We prove that each homothet of that is contained in can be obtained using this operator. A variety of convex subsets of with interesting combinatorial properties can also be obtained. For example, this operator can assign a regular dodecagon to the 4-element set consisting of the vertices and the orthocenter of an equilateral …


The Planet, 2007, Winter, Shawn C. Query, Huxley College Of The Environment, Western Washington University Jan 2007

The Planet, 2007, Winter, Shawn C. Query, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.


Excess Silica In Omphacite And The Formation Of Free Silica In Eclogite, H. W. Day, Sean R. Mulcahy Jan 2007

Excess Silica In Omphacite And The Formation Of Free Silica In Eclogite, H. W. Day, Sean R. Mulcahy

Geology Faculty Publications

Silica lamellae in eclogitic clinopyroxene are widely interpreted as evidence of exsolution during decompression of eclogite. However, mechanisms other than exsolution might produce free silica, and the possible mechanisms depend in part on the nature and definition of excess silica. ‘Excess’ silica may occur in both stoichiometric and non-stoichiometric pyroxene. Although the issue has been debated, we show that all common definitions of excess silica in non-stoichiometric clinopyroxene are internally consistent, interchangeable, and therefore equivalent. The excess silica content of pyroxene is easily illustrated in a three-component, condensed composition space and may be plotted directly from a structural formula unit …


Precursory Seismicity Associated With Frequent, Large Ice Avalanches On Iliamna Volcano, Alaska, Usa, Jacqueline Caplan-Auerbach, Christian Huggel Jan 2007

Precursory Seismicity Associated With Frequent, Large Ice Avalanches On Iliamna Volcano, Alaska, Usa, Jacqueline Caplan-Auerbach, Christian Huggel

Geology Faculty Publications

Since 1994, at least six major (volume >106m3 ) ice and rock avalanches have occurred on Iliamna volcano, Alaska, USA. Each of the avalanches was preceded by up to 2 hours of seismicity believed to represent the initial stages of failure. Each seismic sequence begins with a series of repeating earthquakes thought to represent slip on an ice–rock interface, or between layers of ice. This stage is followed by a prolonged period of continuous ground-shaking that reflects constant slip accommodated by deformation at the glacier base. Finally the glacier fails in a large avalanche. Some of the events appear to …


Pleistocene Brawley And Ocotillo Formations: Evidence For Initial Strike-Slip Deformation Along The San Felipe And San Jacinto Fault Zones, Southern California, Stefan M. Kirby, Susanne U. Janecke, Rebecca J. Dorsey, Bernard A. Housen, Victoria E. Langenheim, Kristin A. Mcdougall, Alexander N. Steely Jan 2007

Pleistocene Brawley And Ocotillo Formations: Evidence For Initial Strike-Slip Deformation Along The San Felipe And San Jacinto Fault Zones, Southern California, Stefan M. Kirby, Susanne U. Janecke, Rebecca J. Dorsey, Bernard A. Housen, Victoria E. Langenheim, Kristin A. Mcdougall, Alexander N. Steely

Geology Faculty Publications

We examine the Pleistocene tectonic reorganization of the Pacific–North American plate boundary in the Salton Trough of southern California with an integrated approach that includes basin analysis, magnetostratigraphy, and geologic mapping of upper Pliocene to Pleistocene sedimentary rocks in the San Felipe Hills. These deposits preserve the earliest sedimentary record of movement on the San Felipe and San Jacinto fault zones that replaced and deactivated the late Cenozoic West Salton detachment fault. Sandstone and mudstone of the Brawley Formation accumulated between ∼1.1 and ∼0.6–0.5 Ma in a delta on the margin of an arid Pleistocene lake, which received sediment from …


Petrographic Signature For The Whidbey Formation, Jonathan Peterson Jan 2007

Petrographic Signature For The Whidbey Formation, Jonathan Peterson

WWU Graduate School Collection

The late Pleistocene Whidbey Formation occupies a region on and around Whidbey Island, Washington, that received both northern-derived glacial sediments and eastern-derived nonglacial sediments. Distinguishing between glacial outwash and nonglacial sediments of the Whidbey Formation and the younger Olympia beds has been problematic where stratigraphic sections are incomplete. For the Whidbey Formation, discontinuous deposits of sand, clay, peat and silt that stem from meandering streams on floodplains have not been fully characterized, petrographically. Recent documentation (Dragovich and others, 2005) of dacitic channel and lahar-runout facies on northern Whidbey Island spurred petrographic analysis of various sands from across the whole region …


Application Of A Nitrate Fate And Transport Model To The Abbotsford-Sumas Aquifer, Whatcom County, Washington, Margo A. Burton Jan 2007

Application Of A Nitrate Fate And Transport Model To The Abbotsford-Sumas Aquifer, Whatcom County, Washington, Margo A. Burton

WWU Graduate School Collection

The Abbotsford-Sumas aquifer is a shallow, unconfined aquifer located in an agriculturally intensive area in northwestern Washington and southwestern British Columbia. Due to aquifer characteristics and surface land use, the Abbotsford-Sumas aquifer has had a history of nitrate contamination from non-point sources. As such, nutrient managers are interested in predictive tools to evaluate management strategies. I assessed the effectiveness of a GIS based nitrate fate and transport model developed specifically for the Abbotsford-Sumas aquifer by Almasri and Kaluarachchi (2004) as a predictive tool for nutrient management. This model couples four sub-models that collectively estimate nutrient loading, predict soil-nitrogen dynamics (NLEAP), …


Shelter Competition Between Native Signal Crayfish And Non-Native Red Swamp Crayfish In Pine Lake, Sammamish, Washington: The Role Of Size And Sex, Karl W. Mueller Jan 2007

Shelter Competition Between Native Signal Crayfish And Non-Native Red Swamp Crayfish In Pine Lake, Sammamish, Washington: The Role Of Size And Sex, Karl W. Mueller

WWU Graduate School Collection

Freshwater crayfish (Decapoda) communities worldwide are becoming increasingly similar from location to location by the intentional or accidental introduction of North American crayfishes. The red swamp crayfish (Procambarus clarkii, Cambaridae), which is native to the south-central United States and northeastern Mexico, is the most widely introduced crayfish in the world. It was first discovered in Pine Lake, Sammamish, Washington in 2000. The results of a 2005 baseline survey of the crayfish in Pine Lake suggested that the red swamp crayfish was displacing the native signal crayfish (Pacifastacus leniusculus, Astacidae). One mechanism through which non-native crayfishes displace native species is competitive …


Quantifying The Glacial Meltwater Component Of Streamflow In The Middle Fork Nooksack River, Whatcom County, Wa, Using A Distributed Hydrology Model, Carrie B. Donnell Jan 2007

Quantifying The Glacial Meltwater Component Of Streamflow In The Middle Fork Nooksack River, Whatcom County, Wa, Using A Distributed Hydrology Model, Carrie B. Donnell

WWU Graduate School Collection

Glacial meltwater is a vital component of rivers and streams in glaciated regions such as the Pacific Northwest, and can be critical for municipal water supplies, power generation, and habitat issues. The Middle Fork of the Nooksack River is fed by meltwater from Deming Glacier on Mount Baker, WA. The City of Bellingham has been diverting water from the Middle Fork since 1962 to supplement the water supply, and to maintain water quality in Lake Whatcom, the water source for the city. Because of regulations, water is only diverted when the Middle Fork exceeds minimum acceptable streamflow. A concern for …


Applicability Of The Nlos Model For Predictions Of Soil Water Movement And Nitrogen Transport In An Agricultural Soil, Agassiz, Bc, Heather R. Hirsch Jan 2007

Applicability Of The Nlos Model For Predictions Of Soil Water Movement And Nitrogen Transport In An Agricultural Soil, Agassiz, Bc, Heather R. Hirsch

WWU Graduate School Collection

The Abbotsford-Sumas aquifer is a shallow, unconfined aquifer in northern Whatcom County, WA and southern British Columbia, Canada that is contaminated with nitrates due to agricultural land use. Currently, conservation managers rely on Post-Harvest Soil Nitrate Tests (PHSNTs) to predict nitrate leaching potential to the aquifer. However, these tests have limitations as an assessment tool because of their inaccuracy. Therefore, US and Canadian government agencies are considering the NLEAP on STELLA (NLOS) leaching model as an additional tool for assessing nutrient management strategies. NLOS is an adaptation of the Nitrogen Leaching and Economic Analysis Package (NLEAP) model. I examined the …


Characteristics And Processes Of Degradation On Normal Fault Scarps In Basalt, Central Oregon And Northern California, Kelsay Davis Jan 2007

Characteristics And Processes Of Degradation On Normal Fault Scarps In Basalt, Central Oregon And Northern California, Kelsay Davis

WWU Graduate School Collection

Normal faults that break the surface create scarps. Scarps in alluvium degrade predictably so that time since formation can be inferred from scarp profile, however, scarps in jointed bedrock, such as basalt, do not degrade according to previous models. Understanding the processes involved in degradation of scarps in jointed basalt may lead to the formation of a degradation model.

I use survey data and statistical analyses from 36 scarps in central Oregon and northern California, to determine the characteristics that play a dominant role in scarp degradation in jointed basalt. These data indicate that scarp facing direction, column height, and …


Oblique Photogrammetric Analysis Of Dome Growth At Mount St. Helens Volcano, 2004 – 2007, Angela K. Diefenbach Jan 2007

Oblique Photogrammetric Analysis Of Dome Growth At Mount St. Helens Volcano, 2004 – 2007, Angela K. Diefenbach

WWU Graduate School Collection

This project is an oblique photogrammetric survey of the 2004-2007 dome-building eruption of Mount St. Helens volcano with two primary objectives: (1) to evaluate the potential of a new rapid and low-cost technique to create digital elevation models (DEMs) and subsequently calculate dome volumes and extrusion rates at Mount St. Helens; and (2) to attempt to understand mechanics associated with lava dome extrusion and collapse by analyzing volumetric and extrusion rate measurements in the context of dome height measurements, seismicity data, and migration of the locus of dome growth.

The new method uses sets of oblique aerial photographs, acquired from …


Lake Samish Monitoring Project 2006 Final Report, Robin A. Matthews, Joan Vandersypen, Kara Hitchko Nov 2006

Lake Samish Monitoring Project 2006 Final Report, Robin A. Matthews, Joan Vandersypen, Kara Hitchko

Lake Samish

Lake Samish is a valuable aquatic resource, providing public access for boating, fishing, swimming, picnicking, and other water and lakeshore activities. Residents around the lake enjoy outstanding views of both the lake and its surrounding watershed, and the lake serves as a water supply for many of the lakeshore residents.

Lake Samish is located in the Washington State Department of Ecology’s water resource inventory area #3 (WRIA 3), and discharges into Friday Creek, a salmon spawning tributary of the Samish River. The Lake Samish monitoring project was initiated in June 2005 to collect monthly water quality data from the lake …


An Exceptional Exponential Function, Branko Ćurgus Nov 2006

An Exceptional Exponential Function, Branko Ćurgus

Mathematics Faculty Publications

We show that there is a link between a standard calculus problem of finding the best view of a painting and special tangent lines to the graphs of exponential functions. Surprisingly, the exponential function with the "best view" is not the one with the base e. A similar link is established for families of functions obtained by composing exponential functions with a fixed linear function. The key tool in the proof is the Lambert W function.


The Planet, 2006, Fall, Shawn C. Query, Huxley College Of The Environment, Western Washington University Oct 2006

The Planet, 2006, Fall, Shawn C. Query, Huxley College Of The Environment, Western Washington University

The Planet

No abstract provided.


Environmental Injustice In Ecuador: Endangered Indigenous Populations And Environmental Degradation, Clover Anneire Muters Oct 2006

Environmental Injustice In Ecuador: Endangered Indigenous Populations And Environmental Degradation, Clover Anneire Muters

WWU Honors College Senior Projects

Nationally and globally there is a widening disparity between the rich and poor which is reflected at every level of society. Environmental injustice is a term to describe the unjust way that natural resources are allocated, and the very real phenomenon of a disproportionate amount of the negative consequences of environmental degradation being placed on those populations that are poor and underrepresented. This paper will address this situation in Ecuador, and specifically, the connection between the environmental degradation of one of the most biologically diverse places in the world, and the destruction of indigenous and repressed populations who have lived …


Congruences For The Coefficients Of Weakly Holomorphic Modular Forms, Stephanie Treneer Sep 2006

Congruences For The Coefficients Of Weakly Holomorphic Modular Forms, Stephanie Treneer

Mathematics Faculty Publications

Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup Γ0 (N). In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.


Temperature Regulation Of Bacterial Production, Respiration, And Growth Efficiency In A Temperate Salt-Marsh Estuary, Jude K. Apple, P. A. Del Giorgio, W. Michael Kemp Jul 2006

Temperature Regulation Of Bacterial Production, Respiration, And Growth Efficiency In A Temperate Salt-Marsh Estuary, Jude K. Apple, P. A. Del Giorgio, W. Michael Kemp

Shannon Point Marine Center Faculty Publications

There is consensus that temperature plays a major role in shaping microbial activity, but there are still questions as to how temperature influences different aspects of bacterioplankton carbon metabolism under different environmental conditions. We examined the temperature dependence of bacterioplankton carbon metabolism, whether this temperature dependence changes at different temperatures, and whether the relationship between temperature and carbon metabolism varies among estuarine sub-systems differing in their degree of enrichment. Two years of intensive sampling in a temperate estuary (Monie Bay, Chesapeake Bay, USA) revealed significant differences in the temperature dependence of bacterial production (BP) and respiration (BR), which drove a …


Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar Jun 2006

Convergence Of Algorithms For Reconstructing Convex Bodies And Directional Measures, Richard J. Gardner, Markus Kiderlen, Peyman Milanfar

Mathematics Faculty Publications

We investigate algorithms for reconstructing a convex body K in Rn from noisy measurements of its support function or its brightness function in k directions u1, . . . , uk. The key idea of these algorithms is to construct a convex polytope Pk whose support function (or brightness function) best approximates the given measurements in the directions u1, . . . , uk (in the least squares sense). The measurement errors are assumed to be stochastically independent and Gaussian. It is shown that this procedure is (strongly) consistent, meaning that, …


Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov May 2006

Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov

Mathematics Faculty Publications

The Cellular Potts Model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. In this paper, we derive continuous limit of discrete one dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are …


Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov May 2006

Multiscale Dynamics Of Biological Cells With Chemotactic Interactions: From A Discrete Stochastic Model To A Continuous Description, Mark Alber, Nan Chen, Tilmann Glimm, Pavel M. Lushnikov

Mathematics Faculty Publications

The cellular Potts model (CPM) has been used for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs, and many others. We derive a continuous limit of a discrete one-dimensional CPM with the chemotactic interactions between cells in the form of a Fokker-Planck equation for the evolution of the cell probability density function. This equation is then reduced to the classical macroscopic Keller-Segel model. In particular, all coefficients of the Keller-Segel model are obtained from parameters of the CPM. Theoretical results are verified …